feat(libraries): add fixed-point and low-level math primitives

src/libraries/FixedPoint128.sol

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+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Q128.128 fixed point constant used by the fee-growth accounting.
+library FixedPoint128 {
+    uint256 internal constant q128 = 0x100000000000000000000000000000000;
+}

src/libraries/FixedPoint96.sol

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+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Q64.96 fixed point constants used by the sqrt-price math.
+library FixedPoint96 {
+    uint8 internal constant resolution = 96;
+    uint256 internal constant q96 = 0x1000000000000000000000000;
+}

src/libraries/SafeCast.sol

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+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Checked narrowing casts between integer widths.
+library SafeCast {
+    function toUint160(uint256 y) internal pure returns (uint160 z) {
+        require((z = uint160(y)) == y, "SafeCast: U160");
+    }
+
+    function toUint128(uint256 y) internal pure returns (uint128 z) {
+        require((z = uint128(y)) == y, "SafeCast: U128");
+    }
+
+    function toInt128(int256 y) internal pure returns (int128 z) {
+        require((z = int128(y)) == y, "SafeCast: I128");
+    }
+
+    function toInt256(uint256 y) internal pure returns (int256 z) {
+        require(y < 2 ** 255, "SafeCast: I256");
+        z = int256(y);
+    }
+}

src/libraries/UnsafeMath.sol

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+// SPDX-License-Identifier: MIT
+pragma solidity 0.8.36;
+
+/// @title Rounding-up integer division that trusts its non-zero denominator.
+library UnsafeMath {
+    function divRoundingUp(uint256 x, uint256 y) internal pure returns (uint256 z) {
+        assembly {
+            z := add(div(x, y), gt(mod(x, y), 0))
+        }
+    }
+}